A Non-Convex Relaxation for Fixed-Rank Approximation
Paper i proceeding, 2017

This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear norm typically work well and come with theoretical performance guarantees. On the other hand these formulations suffer from a shrinking bias that can severely degrade the solution in the presence of noise. In this theoretical paper we study an alternative non-convex relaxation that in contrast to the nuclear norm does not penalize the leading singular values and thereby avoids this bias. We show that despite its non-convexity the proposed formulation will in many cases have a single stationary point if a RIP holds. Our numerical tests show that our approach typically converges to a better solution than nuclear norm based alternatives even in cases when the RIP does not hold.


Carl Olsson

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik, Digitala bildsystem och bildanalys

Marcus Carlsson

Lunds universitet

Erik Bylow

Lunds universitet

IEEE International Conference on Computer Vision Workshops

2473-9936 (ISSN)


16th IEEE International Conference on Computer Vision (ICCV)
Venice, Italy,


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